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This paper formulates face labeling as a conditional random field with unary and pairwise classifiers. We develop a novel multi-objective learning method that optimizes a single unified deep convolutional network with two distinct non-structured loss functions: one encoding the unary label likelihoods and the other encoding the pairwise label dependencies. Moreover, we regularize the network by using a nonparametric prior as new input channels in addition to the RGB image, and show that significant performance improvements can be achieved with a much smaller network size. Experiments on both the LFW and Helen datasets demonstrate state-of-the-art results of the proposed algorithm, and accurate labeling results on challenging images can be obtained by the proposed algorithm for real-world applications.